Problem: Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold: 

  * Aij = Aji, for all i, j (1 ≤ i, j ≤ n); 
  * Bij = - Bji, for all i, j (1 ≤ i, j ≤ n); 
  * Wij = Aij + Bij, for all i, j (1 ≤ i, j ≤ n). 



Can you solve the problem?

Input

The first line contains an integer n (1 ≤ n ≤ 170). Each of the following n lines contains n integers. The j-th integer in the i-th line is Wij (0 ≤ |Wij| < 1717).

Output

The first n lines must contain matrix A. The next n lines must contain matrix B. Print the matrices in the format equal to format of matrix W in input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Examples

Input

2
1 4
3 2


Output

1.00000000 3.50000000
3.50000000 2.00000000
0.00000000 0.50000000
-0.50000000 0.00000000


Input

3
1 2 3
4 5 6
7 8 9


Output

1.00000000 3.00000000 5.00000000
3.00000000 5.00000000 7.00000000
5.00000000 7.00000000 9.00000000
0.00000000 -1.00000000 -2.00000000
1.00000000 0.00000000 -1.00000000
2.00000000 1.00000000 0.00000000

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class CP {
	public static void main(String[] args) throws Exception {
		FastReader s = new FastReader();
		int n = s.nextInt();
		float[][] a = new float[n][n];
		float[][] b = new float[n][n];
		for(int i=0;i<n;i++) for(int j=0;j<n;j++) a[i][j]=s.nextInt();
		for(int i=0;i<n;i++) for(int j=0;j<n;j++) b[i][j]=a[j][i];
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<n;j++) System.out.print((a[i][j]+b[i][j])/2 + " "); 
			System.out.println();			
		}
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<n;j++) System.out.print((a[i][j]-b[i][j])/2 + " "); 
			System.out.println();			
		}
	}

	static class FastReader {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(
                new InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
 
        long nextLong() { return Long.parseLong(next()); }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
	
	class Pair<S extends Comparable<S>, T extends Comparable<T>> implements Comparable<Pair<S, T>> {
	    S first;
	    T second;
	    
	    Pair(S f, T s) {
	        first = f;
	        second = s;
	    }
	 
	    @Override
	    public int compareTo(Pair<S, T> o) {
	        int t = first.compareTo(o.first);
	        if (t == 0) return second.compareTo(o.second);
	        return t;
	    }
	    
	    @Override
	    public int hashCode() {
	        return (31 + first.hashCode()) * 31 + second.hashCode();
	    }
	    
	    @Override
	    public boolean equals(Object o) {
	        if (!(o instanceof Pair)) return false;
	        if (o == this) return true;
	        Pair p = (Pair) o;
	        return first.equals(p.first) && second.equals(p.second);
	    }
	    
	    @Override
	    public String toString() {
	        return "Pair{" + first + ", " + second + "}";
	    }
	}
}